Answer:
length = 6 yards
width = 3.5 yards
Step-by-step explanation:
the length of a rectangle is 1 yard less than twice the width
LEt 'w' be the width of the rectangle
and 'l' be the length of the rectangle
length l = 2 times the width -1
so l = 2w -1
Area of the rectangle = length * width
Area = l * w
we know length is 2w-1 and given area = 21
21 = (2w-1) * w
[tex]21= 2w^2 - w[/tex]
subtract 21 on both sides
[tex]0= 2w^2 - w - 21[/tex]
now solve for 'w'
[tex]0= 2w^2 +6w -7w- 21[/tex]
0 = 2w(w+3)-7(w+3)
0= (2w-7)(w+3)
2w-7 = 0 and w+3 =0
w = 7/2 w=-3
width cannot be negative so we ignore w=-3
width w= 3.5
length = 2w-1= 2(3.5) - 1= 7-1=6
length = 6 yards
